##############ECHO OF PROBLEM################# ##############temp/arccos_cos_1d3_1d1postode.ode################# diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(1.3) x_end=c(1.1) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_display_interval=0.001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(x)*c(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 1.2990000000000002 y[1] (closed_form) 0.8437005000000002 y[1] (numeric) 0.8437004999536891 absolute error 4.631106609309654e-11 relative error 5.489040968103792e-09% Desired digits 8 Estimated correct digits 14 Correct digits 11 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2980000000000003 y[1] (closed_form) 0.8424020000000003 y[1] (numeric) 0.8424019999071987 absolute error 9.280165524927497e-11 relative error 1.1016314686963581e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2970000000000004 y[1] (closed_form) 0.8411045000000005 y[1] (numeric) 0.8411044998605285 absolute error 1.3947198951314022e-10 relative error 1.6582004912961486e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2960000000000005 y[1] (closed_form) 0.8398080000000007 y[1] (numeric) 0.8398079998136786 absolute error 1.8632206888469227e-10 relative error 2.2186269824137436e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2950000000000006 y[1] (closed_form) 0.8385125000000008 y[1] (numeric) 0.8385124997666488 absolute error 2.333520043862336e-10 relative error 2.7829281541567165e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2940000000000007 y[1] (closed_form) 0.8372180000000009 y[1] (numeric) 0.837217999719439 absolute error 2.8056190704006667e-10 relative error 3.351121297440647e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2930000000000008 y[1] (closed_form) 0.8359245000000011 y[1] (numeric) 0.8359244996720492 absolute error 3.2795188786849394e-10 relative error 3.92322378239295e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.292000000000001 y[1] (closed_form) 0.8346320000000012 y[1] (numeric) 0.8346319996244792 absolute error 3.755219468715154e-10 relative error 4.499251728564384e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.291000000000001 y[1] (closed_form) 0.8333405000000014 y[1] (numeric) 0.833340499576729 absolute error 4.2327241711603847e-10 relative error 5.0792253240546664e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2900000000000011 y[1] (closed_form) 0.8320500000000015 y[1] (numeric) 0.8320499995287983 absolute error 4.712031875797607e-10 relative error 5.663159516612701e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2890000000000013 y[1] (closed_form) 0.8307605000000016 y[1] (numeric) 0.8307604994806872 absolute error 5.193143692849844e-10 relative error 6.251071991085077e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2880000000000014 y[1] (closed_form) 0.8294720000000018 y[1] (numeric) 0.8294719994323955 absolute error 5.676062952986172e-10 relative error 6.842983190494869e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2870000000000015 y[1] (closed_form) 0.8281845000000019 y[1] (numeric) 0.8281844993839231 absolute error 6.16078743576054e-10 relative error 7.438906953415e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2860000000000016 y[1] (closed_form) 0.826898000000002 y[1] (numeric) 0.82689799933527 absolute error 6.647320471842022e-10 relative error 8.038863888704538e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2850000000000017 y[1] (closed_form) 0.8256125000000022 y[1] (numeric) 0.8256124992864359 absolute error 7.135663171453643e-10 relative error 8.642872014962982e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2840000000000018 y[1] (closed_form) 0.8243280000000023 y[1] (numeric) 0.8243279992374208 absolute error 7.625814424372379e-10 relative error 9.250946740099036e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.283000000000002 y[1] (closed_form) 0.8230445000000025 y[1] (numeric) 0.8230444991882246 absolute error 8.117778671490328e-10 relative error 9.863110283211057e-08% Desired digits 8 Estimated correct digits 13 Correct digits 10 h -0.001 TOP MAIN SOLVE Loop x[1] 1.282000000000002 y[1] (closed_form) 0.8217620000000025 y[1] (numeric) 0.8217619991388473 absolute error 8.611552582138415e-10 relative error 1.0479375515220208e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2810000000000021 y[1] (closed_form) 0.8204805000000027 y[1] (numeric) 0.8204804990892886 absolute error 9.107141707431765e-10 relative error 1.1099766182659715e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2800000000000022 y[1] (closed_form) 0.8192000000000029 y[1] (numeric) 0.8191999990395484 absolute error 9.604544937147352e-10 relative error 1.1724298018978659e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2790000000000024 y[1] (closed_form) 0.817920500000003 y[1] (numeric) 0.8179204989896267 absolute error 1.0103763381508202e-09 relative error 1.235298954055824e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2780000000000025 y[1] (closed_form) 0.8166420000000032 y[1] (numeric) 0.8166419989395234 absolute error 1.0604798150737338e-09 relative error 1.298585934930765e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2770000000000026 y[1] (closed_form) 0.8153645000000033 y[1] (numeric) 0.8153644988892382 absolute error 1.1107650355057785e-09 relative error 1.3622926133107023e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2760000000000027 y[1] (closed_form) 0.8140880000000035 y[1] (numeric) 0.8140879988387713 absolute error 1.1612322214915594e-09 relative error 1.4264210030015852e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2750000000000028 y[1] (closed_form) 0.8128125000000036 y[1] (numeric) 0.8128124987881223 absolute error 1.2118812620087738e-09 relative error 1.4909727175809531e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.274000000000003 y[1] (closed_form) 0.8115380000000038 y[1] (numeric) 0.8115379987372913 absolute error 1.2627124901243292e-09 relative error 1.5559499248640524e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.273000000000003 y[1] (closed_form) 0.8102645000000038 y[1] (numeric) 0.810264498686278 absolute error 1.3137257948159231e-09 relative error 1.6213542550808e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2720000000000031 y[1] (closed_form) 0.8089920000000039 y[1] (numeric) 0.8089919986350824 absolute error 1.364921509150463e-09 relative error 1.6871878945038472e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2710000000000032 y[1] (closed_form) 0.8077205000000042 y[1] (numeric) 0.8077204985837044 absolute error 1.4162997441502512e-09 relative error 1.753452765096644e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2700000000000033 y[1] (closed_form) 0.8064500000000042 y[1] (numeric) 0.8064499985321439 absolute error 1.4678602777706828e-09 relative error 1.8201503847364067e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2690000000000035 y[1] (closed_form) 0.8051805000000044 y[1] (numeric) 0.8051804984804007 absolute error 1.5196036651232703e-09 relative error 1.8872832428545673e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2680000000000036 y[1] (closed_form) 0.8039120000000045 y[1] (numeric) 0.8039119984284748 absolute error 1.5715296841634085e-09 relative error 1.9548528746472247e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2670000000000037 y[1] (closed_form) 0.8026445000000046 y[1] (numeric) 0.802644498376366 absolute error 1.623638667958005e-09 relative error 2.0228615133574026e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2660000000000038 y[1] (closed_form) 0.8013780000000048 y[1] (numeric) 0.8013779983240742 absolute error 1.6759306165070598e-09 relative error 2.0913109874579158e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.265000000000004 y[1] (closed_form) 0.8001125000000049 y[1] (numeric) 0.8001124982715992 absolute error 1.7284056408328752e-09 relative error 2.1602032724558918e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.264000000000004 y[1] (closed_form) 0.7988480000000051 y[1] (numeric) 0.7988479982189411 absolute error 1.7810639629800562e-09 relative error 2.2295404920335844e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2630000000000041 y[1] (closed_form) 0.7975845000000052 y[1] (numeric) 0.7975844981660997 absolute error 1.8339055829486028e-09 relative error 2.2993245016027654e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2620000000000042 y[1] (closed_form) 0.7963220000000053 y[1] (numeric) 0.7963219981130748 absolute error 1.886930500738515e-09 relative error 2.369557164989166e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2610000000000043 y[1] (closed_form) 0.7950605000000055 y[1] (numeric) 0.7950604980598663 absolute error 1.940139160439003e-09 relative error 2.440240913036164e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2600000000000044 y[1] (closed_form) 0.7938000000000056 y[1] (numeric) 0.7937999980064742 absolute error 1.9935314510277635e-09 relative error 2.511377489326971e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2590000000000046 y[1] (closed_form) 0.7925405000000058 y[1] (numeric) 0.7925404979528982 absolute error 2.047107594549402e-09 relative error 2.5829690653656025e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2580000000000047 y[1] (closed_form) 0.7912820000000059 y[1] (numeric) 0.7912819978991382 absolute error 2.100867702026221e-09 relative error 2.6550176827303106e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2570000000000048 y[1] (closed_form) 0.790024500000006 y[1] (numeric) 0.7900244978451944 absolute error 2.154811662435918e-09 relative error 2.7275251114818614e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.256000000000005 y[1] (closed_form) 0.7887680000000061 y[1] (numeric) 0.7887679977910663 absolute error 2.2089398088454004e-09 relative error 2.8004936924994207e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.255000000000005 y[1] (closed_form) 0.7875125000000063 y[1] (numeric) 0.7875124977367539 absolute error 2.263252363299273e-09 relative error 2.873925637115925e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.254000000000005 y[1] (closed_form) 0.7862580000000065 y[1] (numeric) 0.7862579976822571 absolute error 2.3177493257975357e-09 relative error 2.9478228848514313e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2530000000000052 y[1] (closed_form) 0.7850045000000065 y[1] (numeric) 0.7850044976275758 absolute error 2.3724306963401887e-09 relative error 3.022187384072536e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2520000000000053 y[1] (closed_form) 0.7837520000000067 y[1] (numeric) 0.78375199757271 absolute error 2.427296696971837e-09 relative error 3.09702137534809e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2510000000000054 y[1] (closed_form) 0.7825005000000068 y[1] (numeric) 0.7825004975176593 absolute error 2.482347549737085e-09 relative error 3.172327109998094e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2500000000000056 y[1] (closed_form) 0.781250000000007 y[1] (numeric) 0.7812499974624237 absolute error 2.5375832546359334e-09 relative error 3.2481065659339656e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2490000000000057 y[1] (closed_form) 0.7800005000000071 y[1] (numeric) 0.7800004974070032 absolute error 2.5930039226906842e-09 relative error 3.324361872448365e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2480000000000058 y[1] (closed_form) 0.7787520000000072 y[1] (numeric) 0.7787519973513974 absolute error 2.6486097759459426e-09 relative error 3.401095311403268e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2470000000000059 y[1] (closed_form) 0.7775045000000074 y[1] (numeric) 0.7775044972956064 absolute error 2.704400925424011e-09 relative error 3.4783090328403053e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.246000000000006 y[1] (closed_form) 0.7762580000000074 y[1] (numeric) 0.7762579972396301 absolute error 2.760377371124889e-09 relative error 3.5560050538929874e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.245000000000006 y[1] (closed_form) 0.7750125000000075 y[1] (numeric) 0.7750124971834682 absolute error 2.8165393350931822e-09 relative error 3.6341856874478215e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2440000000000062 y[1] (closed_form) 0.7737680000000078 y[1] (numeric) 0.7737679971271207 absolute error 2.872887039373495e-09 relative error 3.7128532575312835e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2430000000000063 y[1] (closed_form) 0.7725245000000078 y[1] (numeric) 0.7725244970705876 absolute error 2.929420261921223e-09 relative error 3.7920095245150066e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2420000000000064 y[1] (closed_form) 0.771282000000008 y[1] (numeric) 0.7712819970138685 absolute error 2.9861395578478778e-09 relative error 3.8716572639421723e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2410000000000065 y[1] (closed_form) 0.7700405000000081 y[1] (numeric) 0.7700404969569634 absolute error 3.043044705108855e-09 relative error 3.9517982562070735e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2400000000000067 y[1] (closed_form) 0.7688000000000083 y[1] (numeric) 0.7687999968998722 absolute error 3.1001360367710618e-09 relative error 4.032435011408726e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2390000000000068 y[1] (closed_form) 0.7675605000000084 y[1] (numeric) 0.7675604968425948 absolute error 3.1574136638568007e-09 relative error 4.1135697627180735e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2380000000000069 y[1] (closed_form) 0.7663220000000085 y[1] (numeric) 0.7663219967851309 absolute error 3.2148775863660717e-09 relative error 4.19520460898426e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.237000000000007 y[1] (closed_form) 0.7650845000000086 y[1] (numeric) 0.7650844967274806 absolute error 3.2725280263434797e-09 relative error 4.2773419489526226e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.236000000000007 y[1] (closed_form) 0.7638480000000087 y[1] (numeric) 0.7638479966696435 absolute error 3.3303652058336297e-09 relative error 4.359984192972413e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2350000000000072 y[1] (closed_form) 0.7626125000000089 y[1] (numeric) 0.7626124966116198 absolute error 3.3883891248365217e-09 relative error 4.4431334718962543e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2340000000000073 y[1] (closed_form) 0.761378000000009 y[1] (numeric) 0.7613779965534091 absolute error 3.446599894374458e-09 relative error 4.526792072235364e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2330000000000074 y[1] (closed_form) 0.7601445000000091 y[1] (numeric) 0.7601444964950114 absolute error 3.5049977364920437e-09 relative error 4.6109624373944716e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2320000000000075 y[1] (closed_form) 0.7589120000000092 y[1] (numeric) 0.7589119964364265 absolute error 3.5635827622115812e-09 relative error 4.695646876332879e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2310000000000076 y[1] (closed_form) 0.7576805000000094 y[1] (numeric) 0.7576804963776543 absolute error 3.622355082555373e-09 relative error 4.780847708968791e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2300000000000078 y[1] (closed_form) 0.7564500000000095 y[1] (numeric) 0.7564499963186947 absolute error 3.6813148085457215e-09 relative error 4.866567266237921e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2290000000000079 y[1] (closed_form) 0.7552205000000096 y[1] (numeric) 0.7552204962595475 absolute error 3.740462162227232e-09 relative error 4.952808037158927e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.228000000000008 y[1] (closed_form) 0.7539920000000098 y[1] (numeric) 0.7539919962002126 absolute error 3.799797143599903e-09 relative error 5.039572228352362e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.227000000000008 y[1] (closed_form) 0.7527645000000099 y[1] (numeric) 0.75276449614069 absolute error 3.859319974708342e-09 relative error 5.126862351649541e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2260000000000082 y[1] (closed_form) 0.75153800000001 y[1] (numeric) 0.7515379960809793 absolute error 3.919030766574849e-09 relative error 5.214680783373292e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2250000000000083 y[1] (closed_form) 0.7503125000000102 y[1] (numeric) 0.7503124960210805 absolute error 3.978929630221728e-09 relative error 5.303029911165913e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2240000000000084 y[1] (closed_form) 0.7490880000000103 y[1] (numeric) 0.7490879959609935 absolute error 4.039016787693583e-09 relative error 5.391912282259932e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2230000000000085 y[1] (closed_form) 0.7478645000000105 y[1] (numeric) 0.7478644959007181 absolute error 4.099292350012718e-09 relative error 5.481330307846756e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2220000000000086 y[1] (closed_form) 0.7466420000000106 y[1] (numeric) 0.7466419958402543 absolute error 4.159756317179131e-09 relative error 5.571286261928838e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2210000000000087 y[1] (closed_form) 0.7454205000000107 y[1] (numeric) 0.7454204957796018 absolute error 4.220408911237428e-09 relative error 5.661782726980767e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2200000000000089 y[1] (closed_form) 0.7442000000000109 y[1] (numeric) 0.7441999957187605 absolute error 4.281250354232213e-09 relative error 5.752822298081364e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.219000000000009 y[1] (closed_form) 0.7429805000000109 y[1] (numeric) 0.7429804956577303 absolute error 4.342280646163488e-09 relative error 5.844407284125793e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.218000000000009 y[1] (closed_form) 0.741762000000011 y[1] (numeric) 0.741761995596511 absolute error 4.403500009075856e-09 relative error 5.936540304135007e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2170000000000092 y[1] (closed_form) 0.7405445000000112 y[1] (numeric) 0.7405444955351026 absolute error 4.46490855399162e-09 relative error 6.029223840014412e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2160000000000093 y[1] (closed_form) 0.7393280000000113 y[1] (numeric) 0.7393279954735048 absolute error 4.526506502955385e-09 relative error 6.122460535723408e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2150000000000094 y[1] (closed_form) 0.7381125000000114 y[1] (numeric) 0.7381124954117175 absolute error 4.5882938559671516e-09 relative error 6.216252747334696e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2140000000000095 y[1] (closed_form) 0.7368980000000116 y[1] (numeric) 0.7368979953497407 absolute error 4.650270946093826e-09 relative error 6.310603293934511e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2130000000000096 y[1] (closed_form) 0.7356845000000117 y[1] (numeric) 0.7356844952875741 absolute error 4.712437662313107e-09 relative error 6.4055144050378e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2120000000000097 y[1] (closed_form) 0.7344720000000118 y[1] (numeric) 0.7344719952252176 absolute error 4.774794226669599e-09 relative error 6.500988773798759e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2110000000000098 y[1] (closed_form) 0.733260500000012 y[1] (numeric) 0.733260495162671 absolute error 4.8373409722302085e-09 relative error 6.59702925799239e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.21000000000001 y[1] (closed_form) 0.7320500000000121 y[1] (numeric) 0.7320499950999343 absolute error 4.900077787972634e-09 relative error 6.693638123041531e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.20900000000001 y[1] (closed_form) 0.7308405000000122 y[1] (numeric) 0.7308404950370072 absolute error 4.963005006963783e-09 relative error 6.790818252359715e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2080000000000102 y[1] (closed_form) 0.7296320000000123 y[1] (numeric) 0.7296319949738896 absolute error 5.026122629203655e-09 relative error 6.888572087303697e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2070000000000103 y[1] (closed_form) 0.7284245000000125 y[1] (numeric) 0.7284244949105815 absolute error 5.089430987759158e-09 relative error 6.986902537955645e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2060000000000104 y[1] (closed_form) 0.7272180000000126 y[1] (numeric) 0.7272179948470826 absolute error 5.152929971607989e-09 relative error 7.085811918307715e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2050000000000105 y[1] (closed_form) 0.7260125000000126 y[1] (numeric) 0.7260124947833928 absolute error 5.216619802794753e-09 relative error 7.185303011717653e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2040000000000106 y[1] (closed_form) 0.7248080000000128 y[1] (numeric) 0.724807994719512 absolute error 5.2805008143863574e-09 relative error 7.285378768427314e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2030000000000107 y[1] (closed_form) 0.7236045000000129 y[1] (numeric) 0.72360449465544 absolute error 5.3445728953605e-09 relative error 7.386041539764339e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.2020000000000108 y[1] (closed_form) 0.722402000000013 y[1] (numeric) 0.7224019945911766 absolute error 5.408836378784088e-09 relative error 7.487294302596049e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.201000000000011 y[1] (closed_form) 0.7212005000000131 y[1] (numeric) 0.7212004945267217 absolute error 5.473291375679423e-09 relative error 7.589139740861693e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.200000000000011 y[1] (closed_form) 0.7200000000000133 y[1] (numeric) 0.7199999944620753 absolute error 5.537937997068809e-09 relative error 7.691580551484315e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1990000000000112 y[1] (closed_form) 0.7188005000000134 y[1] (numeric) 0.718800494397237 absolute error 5.602776353974548e-09 relative error 7.794619444441738e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1980000000000113 y[1] (closed_form) 0.7176020000000135 y[1] (numeric) 0.7176019943322068 absolute error 5.667806668441244e-09 relative error 7.898259297550924e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1970000000000114 y[1] (closed_form) 0.7164045000000137 y[1] (numeric) 0.7164044942669846 absolute error 5.733029051491201e-09 relative error 8.002502847889833e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1960000000000115 y[1] (closed_form) 0.7152080000000137 y[1] (numeric) 0.7152079942015701 absolute error 5.79844361414672e-09 relative error 8.107352845810741e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1950000000000116 y[1] (closed_form) 0.7140125000000138 y[1] (numeric) 0.7140124941359632 absolute error 5.864050578452407e-09 relative error 8.212812210503728e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1940000000000117 y[1] (closed_form) 0.7128180000000139 y[1] (numeric) 0.7128179940701638 absolute error 5.929850166452866e-09 relative error 8.318883875621476e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1930000000000118 y[1] (closed_form) 0.7116245000000141 y[1] (numeric) 0.7116244940041716 absolute error 5.9958424891704e-09 relative error 8.425570633347055e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.192000000000012 y[1] (closed_form) 0.7104320000000143 y[1] (numeric) 0.7104319939379866 absolute error 6.062027657627311e-09 relative error 8.53287528943965e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.191000000000012 y[1] (closed_form) 0.7092405000000144 y[1] (numeric) 0.7092404938716087 absolute error 6.1284056718236e-09 relative error 8.640800506772352e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1900000000000122 y[1] (closed_form) 0.7080500000000145 y[1] (numeric) 0.7080499938050376 absolute error 6.194976864826174e-09 relative error 8.749349431291642e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1890000000000123 y[1] (closed_form) 0.7068605000000145 y[1] (numeric) 0.7068604937382732 absolute error 6.261741347657335e-09 relative error 8.858524910724543e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1880000000000124 y[1] (closed_form) 0.7056720000000147 y[1] (numeric) 0.7056719936713154 absolute error 6.328699342361688e-09 relative error 8.968329964008145e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1870000000000125 y[1] (closed_form) 0.7044845000000148 y[1] (numeric) 0.7044844936041639 absolute error 6.395850959961535e-09 relative error 9.078767467504822e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1860000000000126 y[1] (closed_form) 0.703298000000015 y[1] (numeric) 0.7032979935368187 absolute error 6.46319631147918e-09 relative error 9.18984031161619e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1850000000000127 y[1] (closed_form) 0.702112500000015 y[1] (numeric) 0.7021124934692795 absolute error 6.5307355079369245e-09 relative error 9.301551400860667e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1840000000000128 y[1] (closed_form) 0.7009280000000152 y[1] (numeric) 0.7009279934015462 absolute error 6.598468993423978e-09 relative error 9.41390412913143e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.183000000000013 y[1] (closed_form) 0.6997445000000153 y[1] (numeric) 0.6997444933336188 absolute error 6.666396545895736e-09 relative error 9.526900955842583e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.182000000000013 y[1] (closed_form) 0.6985620000000154 y[1] (numeric) 0.6985619932654968 absolute error 6.734518609441409e-09 relative error 9.640545305128622e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1810000000000132 y[1] (closed_form) 0.6973805000000155 y[1] (numeric) 0.6973804931971804 absolute error 6.802835073038693e-09 relative error 9.754839822791922e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1800000000000133 y[1] (closed_form) 0.6962000000000157 y[1] (numeric) 0.6961999931286693 absolute error 6.871346380776799e-09 relative error 9.869787964344506e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1790000000000134 y[1] (closed_form) 0.6950205000000158 y[1] (numeric) 0.6950204930599633 absolute error 6.940052532655727e-09 relative error 9.985392564184177e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1780000000000135 y[1] (closed_form) 0.6938420000000158 y[1] (numeric) 0.6938419929910622 absolute error 7.008953639697779e-09 relative error 1.010165663032451e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1770000000000136 y[1] (closed_form) 0.692664500000016 y[1] (numeric) 0.692664492921966 absolute error 7.078050034969863e-09 relative error 1.0218583506112554e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1760000000000137 y[1] (closed_form) 0.6914880000000161 y[1] (numeric) 0.6914879928526744 absolute error 7.147341718471978e-09 relative error 1.0336176070259804e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1750000000000138 y[1] (closed_form) 0.6903125000000162 y[1] (numeric) 0.6903124927831872 absolute error 7.216829023271032e-09 relative error 1.0454437697812024e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.174000000000014 y[1] (closed_form) 0.6891380000000163 y[1] (numeric) 0.6891379927135044 absolute error 7.286511949367025e-09 relative error 1.0573371297718094e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.173000000000014 y[1] (closed_form) 0.6879645000000164 y[1] (numeric) 0.6879644926436257 absolute error 7.356390718804562e-09 relative error 1.0692980115695485e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1720000000000141 y[1] (closed_form) 0.6867920000000166 y[1] (numeric) 0.6867919925735511 absolute error 7.4264655536282476e-09 relative error 1.0813267413755647e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1710000000000143 y[1] (closed_form) 0.6856205000000167 y[1] (numeric) 0.6856204925032802 absolute error 7.496736564860385e-09 relative error 1.093423630836622e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1700000000000144 y[1] (closed_form) 0.6844500000000168 y[1] (numeric) 0.684449992432813 absolute error 7.567203752500973e-09 relative error 1.1055889769158869e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1690000000000145 y[1] (closed_form) 0.6832805000000169 y[1] (numeric) 0.6832804923621493 absolute error 7.637867671661525e-09 relative error 1.1178231592532402e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1680000000000146 y[1] (closed_form) 0.682112000000017 y[1] (numeric) 0.6821119922912889 absolute error 7.708728100297435e-09 relative error 1.1301264455539914e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1670000000000147 y[1] (closed_form) 0.6809445000000172 y[1] (numeric) 0.6809444922202317 absolute error 7.779785482497914e-09 relative error 1.1424992025778486e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1660000000000148 y[1] (closed_form) 0.6797780000000173 y[1] (numeric) 0.6797779921489775 absolute error 7.851039818262961e-09 relative error 1.154941733663455e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.165000000000015 y[1] (closed_form) 0.6786125000000174 y[1] (numeric) 0.678612492077526 absolute error 7.922491329637182e-09 relative error 1.1674543763395132e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.164000000000015 y[1] (closed_form) 0.6774480000000175 y[1] (numeric) 0.6774479920058772 absolute error 7.994140238665182e-09 relative error 1.1800374698375337e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1630000000000151 y[1] (closed_form) 0.6762845000000176 y[1] (numeric) 0.676284491934031 absolute error 8.065986656369262e-09 relative error 1.192691338684984e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1620000000000152 y[1] (closed_form) 0.6751220000000178 y[1] (numeric) 0.675121991861987 absolute error 8.138030804794028e-09 relative error 1.205416325463222e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1610000000000154 y[1] (closed_form) 0.6739605000000178 y[1] (numeric) 0.6739604917897452 absolute error 8.210272683939479e-09 relative error 1.2182127415388976e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1600000000000155 y[1] (closed_form) 0.6728000000000179 y[1] (numeric) 0.6727999917173053 absolute error 8.282712626872524e-09 relative error 1.2310809492973102e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1590000000000156 y[1] (closed_form) 0.6716405000000181 y[1] (numeric) 0.6716404916446672 absolute error 8.355350855637766e-09 relative error 1.2440212964580816e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1580000000000157 y[1] (closed_form) 0.6704820000000181 y[1] (numeric) 0.6704819915718307 absolute error 8.428187370235207e-09 relative error 1.2570340993844697e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1570000000000158 y[1] (closed_form) 0.6693245000000183 y[1] (numeric) 0.6693244914987958 absolute error 8.501222503731753e-09 relative error 1.2701197257431217e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.156000000000016 y[1] (closed_form) 0.6681680000000184 y[1] (numeric) 0.668167991425562 absolute error 8.574456367149708e-09 relative error 1.2832785118637035e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.155000000000016 y[1] (closed_form) 0.6670125000000185 y[1] (numeric) 0.6670124913521295 absolute error 8.647889071511372e-09 relative error 1.2965107957513738e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1540000000000161 y[1] (closed_form) 0.6658580000000186 y[1] (numeric) 0.6658579912784978 absolute error 8.721520838861352e-09 relative error 1.3098169337698291e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1530000000000162 y[1] (closed_form) 0.6647045000000187 y[1] (numeric) 0.6647044912046668 absolute error 8.795351891244252e-09 relative error 1.3231972840930074e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1520000000000163 y[1] (closed_form) 0.6635520000000188 y[1] (numeric) 0.6635519911306365 absolute error 8.869382339682375e-09 relative error 1.3366521899839234e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1510000000000165 y[1] (closed_form) 0.6624005000000189 y[1] (numeric) 0.6624004910564065 absolute error 8.943612406220325e-09 relative error 1.350182013180858e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1500000000000166 y[1] (closed_form) 0.6612500000000191 y[1] (numeric) 0.6612499909819768 absolute error 9.018042312902708e-09 relative error 1.36378711726313e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1490000000000167 y[1] (closed_form) 0.6601005000000192 y[1] (numeric) 0.6601004909073471 absolute error 9.092672059729523e-09 relative error 1.3774678340236461e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1480000000000168 y[1] (closed_form) 0.6589520000000193 y[1] (numeric) 0.6589519908325173 absolute error 9.167501979767678e-09 relative error 1.3912245474279476e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.147000000000017 y[1] (closed_form) 0.6578045000000193 y[1] (numeric) 0.6578044907574871 absolute error 9.242532184039476e-09 relative error 1.405057609675702e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.146000000000017 y[1] (closed_form) 0.6566580000000195 y[1] (numeric) 0.6566579906822565 absolute error 9.317763005611823e-09 relative error 1.4189674085462365e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1450000000000171 y[1] (closed_form) 0.6555125000000196 y[1] (numeric) 0.6555124906068251 absolute error 9.39319444448472e-09 relative error 1.432954283020452e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1440000000000172 y[1] (closed_form) 0.6543680000000197 y[1] (numeric) 0.654367990531193 absolute error 9.468826722702772e-09 relative error 1.447018607679851e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1430000000000173 y[1] (closed_form) 0.6532245000000199 y[1] (numeric) 0.6532244904553598 absolute error 9.544660062310584e-09 relative error 1.4611607590208717e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1420000000000174 y[1] (closed_form) 0.6520820000000199 y[1] (numeric) 0.6520819903793253 absolute error 9.620694574330457e-09 relative error 1.4753810984400986e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1410000000000176 y[1] (closed_form) 0.65094050000002 y[1] (numeric) 0.6509404903030895 absolute error 9.696930480806998e-09 relative error 1.4896800062074337e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1400000000000177 y[1] (closed_form) 0.6498000000000201 y[1] (numeric) 0.6497999902266521 absolute error 9.77336800378481e-09 relative error 1.504057864540552e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1390000000000178 y[1] (closed_form) 0.6486605000000203 y[1] (numeric) 0.6486604901500129 absolute error 9.8500073653085e-09 relative error 1.5185150576161477e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1380000000000179 y[1] (closed_form) 0.6475220000000204 y[1] (numeric) 0.6475219900731718 absolute error 9.926848565378066e-09 relative error 1.5330519372898147e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.137000000000018 y[1] (closed_form) 0.6463845000000205 y[1] (numeric) 0.6463844899961285 absolute error 1.0003891937060416e-08 relative error 1.547668908685171e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.136000000000018 y[1] (closed_form) 0.6452480000000206 y[1] (numeric) 0.6452479899188829 absolute error 1.0081137702400156e-08 relative error 1.562366361832944e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1350000000000182 y[1] (closed_form) 0.6441125000000206 y[1] (numeric) 0.6441124898414347 absolute error 1.0158585972419587e-08 relative error 1.577144671531644e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1340000000000183 y[1] (closed_form) 0.6429780000000208 y[1] (numeric) 0.6429779897637837 absolute error 1.0236237080185617e-08 relative error 1.5920042490077866e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1330000000000184 y[1] (closed_form) 0.6418445000000209 y[1] (numeric) 0.6418444896859299 absolute error 1.0314091025698247e-08 relative error 1.6069454557447966e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1320000000000185 y[1] (closed_form) 0.640712000000021 y[1] (numeric) 0.640711989607873 absolute error 1.039214803100208e-08 relative error 1.6219686896767562e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1310000000000187 y[1] (closed_form) 0.6395805000000211 y[1] (numeric) 0.6395804895296129 absolute error 1.047040820711942e-08 relative error 1.6370743334293453e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1300000000000188 y[1] (closed_form) 0.6384500000000212 y[1] (numeric) 0.6384499894511493 absolute error 1.0548871887117173e-08 relative error 1.652262806346123e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1290000000000189 y[1] (closed_form) 0.6373205000000213 y[1] (numeric) 0.637320489372482 absolute error 1.0627539293039945e-08 relative error 1.6675345125473901e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.128000000000019 y[1] (closed_form) 0.6361920000000214 y[1] (numeric) 0.6361919892936109 absolute error 1.0706410535910038e-08 relative error 1.6828898407885792e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.127000000000019 y[1] (closed_form) 0.6350645000000216 y[1] (numeric) 0.6350644892145356 absolute error 1.078548594879436e-08 relative error 1.6983292167636506e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1260000000000192 y[1] (closed_form) 0.6339380000000217 y[1] (numeric) 0.6339379891352562 absolute error 1.0864765420670608e-08 relative error 1.7138529983484562e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1250000000000193 y[1] (closed_form) 0.6328125000000218 y[1] (numeric) 0.6328124890557724 absolute error 1.0944249395627992e-08 relative error 1.7294616328893023e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1240000000000194 y[1] (closed_form) 0.6316880000000218 y[1] (numeric) 0.6316879889760838 absolute error 1.1023937984688814e-08 relative error 1.745155517389666e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1230000000000195 y[1] (closed_form) 0.630564500000022 y[1] (numeric) 0.6305644888961904 absolute error 1.1103831520919982e-08 relative error 1.7609350860886708e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1220000000000196 y[1] (closed_form) 0.629442000000022 y[1] (numeric) 0.629441988816092 absolute error 1.1183930004321496e-08 relative error 1.7768007225957443e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1210000000000198 y[1] (closed_form) 0.6283205000000222 y[1] (numeric) 0.6283204887357885 absolute error 1.1264233656937961e-08 relative error 1.792752847780323e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1200000000000199 y[1] (closed_form) 0.6272000000000223 y[1] (numeric) 0.6271999886552795 absolute error 1.1344742811836284e-08 relative error 1.8087919023973023e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.11900000000002 y[1] (closed_form) 0.6260805000000224 y[1] (numeric) 0.6260804885745649 absolute error 1.1425457469016465e-08 relative error 1.824918276326456e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.11800000000002 y[1] (closed_form) 0.6249620000000224 y[1] (numeric) 0.6249619884936445 absolute error 1.1506377961545411e-08 relative error 1.8411324146980133e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1170000000000202 y[1] (closed_form) 0.6238445000000226 y[1] (numeric) 0.623844488412518 absolute error 1.1587504511467728e-08 relative error 1.8574347471953842e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1160000000000203 y[1] (closed_form) 0.6227280000000227 y[1] (numeric) 0.6227279883311854 absolute error 1.166883734082802e-08 relative error 1.8738257057379136e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1150000000000204 y[1] (closed_form) 0.6216125000000228 y[1] (numeric) 0.6216124882496463 absolute error 1.1750376449626287e-08 relative error 1.8903056887732884e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1140000000000205 y[1] (closed_form) 0.6204980000000229 y[1] (numeric) 0.6204979881679006 absolute error 1.183212228195174e-08 relative error 1.9068751683246851e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1130000000000206 y[1] (closed_form) 0.619384500000023 y[1] (numeric) 0.619384488085948 absolute error 1.191407494882668e-08 relative error 1.923534565173368e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1120000000000207 y[1] (closed_form) 0.618272000000023 y[1] (numeric) 0.6182719880037885 absolute error 1.1996234561273411e-08 relative error 1.9402843022606497e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1110000000000209 y[1] (closed_form) 0.6171605000000232 y[1] (numeric) 0.6171604879214216 absolute error 1.2078601563381142e-08 relative error 1.9571248586681566e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.110000000000021 y[1] (closed_form) 0.6160500000000233 y[1] (numeric) 0.6160499878388475 absolute error 1.216117584412757e-08 relative error 1.9740566259438534e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.109000000000021 y[1] (closed_form) 0.6149405000000234 y[1] (numeric) 0.6149404877560656 absolute error 1.2243957847601905e-08 relative error 1.991080087846131e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1080000000000212 y[1] (closed_form) 0.6138320000000235 y[1] (numeric) 0.6138319876730759 absolute error 1.2326947573804148e-08 relative error 2.0081956583892136e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1070000000000213 y[1] (closed_form) 0.6127245000000235 y[1] (numeric) 0.6127244875898782 absolute error 1.2410145355801205e-08 relative error 2.02540380804109e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1060000000000214 y[1] (closed_form) 0.6116180000000236 y[1] (numeric) 0.6116179875064722 absolute error 1.2493551415637683e-08 relative error 2.0427049916184937e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1050000000000215 y[1] (closed_form) 0.6105125000000238 y[1] (numeric) 0.6105124874228578 absolute error 1.2577165975358184e-08 relative error 2.060099666322589e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1040000000000216 y[1] (closed_form) 0.6094080000000239 y[1] (numeric) 0.6094079873390347 absolute error 1.2660989257007316e-08 relative error 2.077588291753114e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1030000000000217 y[1] (closed_form) 0.608304500000024 y[1] (numeric) 0.6083044872550026 absolute error 1.2745021371607379e-08 relative error 2.0951713116715193e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.1020000000000219 y[1] (closed_form) 0.6072020000000241 y[1] (numeric) 0.6072019871707615 absolute error 1.2829262652225282e-08 relative error 2.1128492087023382e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.101000000000022 y[1] (closed_form) 0.6061005000000241 y[1] (numeric) 0.606100487086311 absolute error 1.2913713098861024e-08 relative error 2.1306224130916425e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 TOP MAIN SOLVE Loop x[1] 1.100000000000022 y[1] (closed_form) 0.6050000000000243 y[1] (numeric) 0.604999987001651 absolute error 1.2998373266626118e-08 relative error 2.148491449029024e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h -0.001 Finished! diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; Iterations 201 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Expected Time Remaining 0 Seconds Optimized Time Remaining 0 Seconds Expected Total Time 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 0.0%